摘要
为提高基于抽样统计的堆芯物理不确定性分析效率,将本征正交分解(POD)法与伽辽金(Galerkin)投影法相结合,研究了基于POD-Galerkin方法的降阶模型在堆芯物理不确定性分析中的应用可行性。以二维两群TWIGL基准题为研究对象,在各物质区群常数的有限次扰动下提取堆芯通量分布的关键变化特征,将全阶中子扩散问题在各变化特征上投影以建立降阶中子扩散模型,并以该降阶模型替代全阶模型开展物质区群常数的不确定性分析。结果表明:降阶与全阶模型计算的k eff数学期望偏差接近1 pcm,并且相比于全阶模型不确定性分析所需的计算时间,将降阶模型构造所需的全阶模型计算时间考虑在内,降阶模型的分析时间仅为其11.48%,极大地提高了不确定性分析的效率。基于拉丁超立方抽样和简单随机抽样的降阶与全阶模型计算的k eff数学期望偏差均小于8 pcm,相同样本量下拉丁超立方抽样结果的误差更小。从TWIGL基准题测试结果来看,在POD-Galerkin降阶建模中,相同样本量下,更建议采用拉丁超立方抽样方法。
In order to improve the efficiency of core physical uncertainty analysis based on sampling statistics,the proper orthogonal decomposition(POD)and Galerkin projection method were combined to study the application feasibility of reduced-order model based on POD-Galerkin method in core physical uncertainty analysis.The two-dimensional two group TWIGL benchmark question was taken as the research object,the key variation characteristics of the core flux distribution were extracted under the finite perturbation of the group constants of each material region,and the full-order neutron diffusion problem was projected on the variation characteristics to establish a reduced-order neutron diffusion model.The reduced-order model was used to replace the full-order model to carry out the uncertainty analysis of the group constants of the material region.The results show that the bias of the mathematical expectation of k eff calculated by reduced-order and full-order models is close to 1 pcm.In addition,compared with the calculation time required for uncertainty analysis of full-order model,the analysis time of reduced-order model(including the calculation time of the full-order model required for the construction of reduced-order model)is only 11.48%,which greatly improves the efficiency of uncertainty analysis.The biases of mathematical expectation of k eff calculated by reduced-order and full-order models based on Latin hypercube sampling and simple random sampling are less than 8 pcm,and under the same sample size,the bias from the Latin hypercube sampling result is smaller.From the TWIGL benchmark test results,under the same sample size,Latin hypercube sampling method is more recommended for POD-Galerkin reduced-order model.
作者
梁鑫源
王毅箴
郝琛
LIANG Xinyuan;WANG Yizhen;HAO Chen(Fundamental Science on Nuclear Safety and Simulation Technology Laboratory,Harbin Engineering University,Harbin 150001,China;Institute of Nuclear and New Energy Technology,Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education,Tsinghua University,Beijing 100084,China)
出处
《原子能科学技术》
EI
CAS
CSCD
北大核心
2023年第8期1584-1591,共8页
Atomic Energy Science and Technology
基金
国家自然科学基金(12075067)。
关键词
降阶模型
本征正交分解
伽辽金投影
不确定性分析
reduced-order model
proper orthogonal decomposition
Galerkin projection
uncertainty analysis
